Test by Bikram | Mock GATE | Test 4 | Question: 19

Question

An $Euler$ circuit of an undirected graph is a circuit in which each edge of the graph appears exactly once. Which of the following undirected graphs must have an $Euler$ circuit ?

1.  A complete graph with $12$ vertices
2.  A complete graph with $13$ vertices
3.  A tree with $13$ vertices

• A.  I and II
• B.  II only
• C.  III only
• D.  I and III

Answer 1

For the graph to be Euler circuit, Degree of every vertex should be even.

In $K13$, degree of each vertex is $12$

So option $B$

Comments

Yes @jatin khachane 1 there wont be euler circuit in a tree. Can we even have a circuit in a tree? 

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No